Search Results (22)

This paper proposes a predefined-time stable neurodynamic approach for solving generalized absolute value equations. In contrast to conventional fixed-time stability methods, the proposed approach provides greater flexibility and broader applicability through the inclusion of an adjustable time parameter. Under appropriate conditions, the method is rigorously proven to converge to the unique solution within a predefined time frame. Finally, numerical simulations are conducted to validate the convergence performance of the proposed neurodynamic method. Full article

The temporal course of neuronal electric activity within brain networks, or neurodynamics, reflects the structural and functional properties of the neuronal populations that generate it. Using intracranial stereo-electroencephalography (sEEG) recordings from the public Montreal Neurological Institute (MNI) atlas, we investigated neurodynamics in the primary motor (M1), somatosensory (S1), and auditory (A1) cortices. We tested whether modifying the Higuchi fractal dimension (HFD) by replacing the Euclidean distance with the Fréchet distance could improve sensitivity to local neurodynamics by incorporating trajectory-based similarities in signal evolution. Using a conservative within-subject approach established in the previous literature, we compared signals recorded from different cortical areas within the same individuals (M1 vs. S1: # of people = 16; M1 vs. A1: # = 9; S1 vs. A1: # = 6). To delve deeper into the new measure’s meaning, it was tested on sequences with known fractal properties, the Brownian motion and the Weierstrass function. Results showed that the newly introduced Fréchet-based HFD (HFDf), similarly to standard HFD, consistently discriminated cortical areas at the intra-subject level, confirming the robustness of fractal dimension as a descriptor of region-specific neurodynamics. Contrary to our hypothesis, HFDf did not provide additional sensitivity across areas and notably, it displayed less evident reduction of values in sleep than awake. While cortical regions may share common governing principles across spatiotemporal scales, these do not necessarily translate into strict similarity in temporal signal morphology. We suggest that these findings support that the free-scale nature of neurodynamics is not a self-similar one. This refinement of quantitative tools for cortical neurodynamic mapping paves the way towards novel tools for neuroimaging-informed neuromodulation strategies. Full article

This paper proposes an adaptive single-layer distributed neurodynamic optimization approach with the penalty method to address a non-smooth pseudoconvex optimization problem with affine equality and inequality constraints in multi-agent systems, where the global objective function for the agents is pseudoconvex but not required to be differentiable. The target of this approach is to optimize the global objective while ensuring compliance with various constraints. The approach avoids the use of additional auxiliary variables, thereby reducing communication bandwidth and computational complexity. Under mild assumptions, the solution of the designed model is bounded for any initial conditions, to enter their respective feasible domains in finite time, and remain within these domains indefinitely. To achieve finite-time consensus in undirected, connected networks for multi-agent systems, a novel consensus mechanism is introduced to ensure that all agents synchronize their states within finite time. By exploiting the unique pseudoconvexity of the global objective function, the solution trajectory converges to the optimal state of the original problem. Furthermore, the effectiveness of the proposed approach is verified through two simulation experiments, and comparisons with four existing algorithms are conducted to demonstrate its superiority in convergence performance. Finally, an economic dispatch problem in power systems is provided as an engineering application to illustrate the practical applicability of the proposed algorithm. Full article

This paper proposes finite-time (FT) and fixed-time (FXT) neurodynamic models with time-varying coefficients for solving inverse quasi-variational inequality problems (IQVIPs). Two projected models with time-dependent gains are developed to enhance convergence speed and transient performance. A nominal model establishes the equivalence between equilibrium points and IQVIP solutions. Under Lipschitz continuity and strong monotonicity assumptions, the existence, uniqueness, and global convergence of the proposed models are ensured. By employing Lyapunov stability theory, finite-time and fixed-time convergence of the continuous-time models are rigorously established, where explicit settling-time bounds independent of initial conditions are derived for the FXT case. Furthermore, the robustness of the proposed models under bounded disturbances is analyzed. To validate the theoretical findings, a discrete-time implementation based on the forward Euler method is developed. Numerical experiments demonstrate that all trajectories converge within a uniform upper bound, showing convergence behavior consistent with the fixed-time characteristics of the continuous-time model. Although the convergence time varies with initial conditions, it remains uniformly bounded, which is consistent with the fixed-time stability characteristics of the continuous-time model. The proposed framework provides a computationally efficient and scalable approach for solving IQVIPs, with potential applications in traffic equilibrium, communication networks, distributed control systems, and multi-agent coordination. Its adaptive structure and fixed-time convergence properties make it particularly suitable for real-time optimization in dynamic and uncertain environments. Full article

Complex-valued time-varying matrix inversion (CTMI) plays a crucial role in many engineering and scientific applications, yet achieving fast and robust solutions while maintaining a simple structure is a challenging task. In this paper, a novel finite-time convergent neurodynamic model (FTCN) is proposed for solving CTMI problems efficiently. Distinct from existing approaches, the FTCN model is developed based on the symmetric operator Frobenius norm, which enables a simplified structure without relying on complicated activation functions or integral terms. Rigorous theoretical analysis is conducted to establish the finite-time convergence of the proposed model under both noise-free and bounded noise conditions. To validate the effectiveness of the proposed FTCN model, comprehensive numerical simulations are performed. The experimental results confirm the global convergence property of the FTCN model and its capability in handling large-dimensional CTMI problems. Furthermore, comparisons with existing models under noisy environments demonstrate the superior performance of the proposed FTCN model. Full article

This study investigates the ongoing electrical activity of local neural networks—referred to as neurodynamics—across 37 anatomically defined brain regions. We analyzed stereotactic intracranial EEG (sEEG) recordings from 106 subjects during wakeful rest, focusing on scale-free (power-law) properties to determine whether distinct brain regions exhibit unique neurodynamic signatures. Results revealed a power-law regime in two frequency ranges (approximately 0.5–4 Hz and 33–80 Hz). Notably, the power-law exponent (slope) in the high-frequency band differed significantly between cortical and subcortical areas (p < 0.01). These findings suggest that local neurodynamics, as reflected in scale-free characteristics, may serve as a functional “fingerprint” for brain region classification. This approach may contribute to functional brain parcellation efforts and offer new insights into the intrinsic organization of neuronal networks as revealed by resting-state activity analysis. Full article

Introduction: Judo is a type of combat sport in which athletes must be able to constantly control their position and maintain a constant dynamic balance to respond to their opponent’s moves. In this scenario, the aim of this systematic review was to evaluate the role of core strength and stability in supporting balance, neuromuscular control, and functional performance-related determinants in judo athletes. Methods: PubMed, Scopus, and Web of Science databases were systematically used for articles published from inception to 4 April 2025, to identify any sort of manuscript indicating judo athletes as its population and core training approaches as the intervention (PROSPERO registry with the code: CRD420251032685). Results: Out of 401 studies, after the removal of 206 duplicates, we screened 195 records. Then, seven articles were included in the systematic review. We found that a strong core might improve balance and neurodynamic control. International-level judokas showed greater trunk extensor strength and less trunk angular displacement. Previous research suggests that core training improves physical fitness, balance, and lower limb recovery; moreover, the lack of core muscle strength might predispose athletes to injury, while solid core stability could ensure good support for the body to perform any movement in a balanced, coordinated, and functional manner. Core stability training and strengthening protocols might also decrease the risk of falling, which could have a beneficial effect on judoka athletes. Conclusions: Despite the wide variety of protocols used for core strengthening, it has been documented that a strong core might improve balance and neurodynamic control of movement during competition. Full article

Traumatic experiences can disrupt one’s sense of safety, self-efficacy, and relationships. Prolonged stress may lead to anxiety, depression, and diminished agency. The embodied, subjective manifestations of trauma call for personalized therapeutic approaches that address symptoms and foster resilience. Group Creative Arts Therapies (CATs) offer relational aesthetic interventions that promote resilience and trauma recovery. Incorporating body-based methods, movement, materials and visual expression, CATs support interoceptive awareness, multisensory integration, embodiment, and emotional–cognitive processing. This article presents a review and conceptual framework of group CAT interventions during wartime, focusing on challenges related to body awareness, self-efficacy, and autobiographical memory. It examines how creative aesthetic approaches help process trauma and strengthen resilience. Drawing on predictive processing accounts of brain function, the article explores the neuropsychological impact of trauma and how creative group work may modulate related brain mechanisms. Creative techniques can foster bodily anchored self-awareness, self-efficacy and processes of traumatic memory reconsolidation. Aesthetic experiences are associated with changes in brain activation and connectivity through processes of embodiment, externalization, and meaning making. On an intrapersonal level, converging evidence highlights the role of sensory and sensorimotor processing, along with the dynamic interplay between Default Mode, Executive Control, and Salience networks, as conceptualized in the Triple Network Model. On an interpersonal level, the literature points to the dynamics of brain and body synchronization, as emerging phenomena during shared creative engagement. These neurodynamics provide a coherent framework for understanding how creative arts-based psychotherapeutic group work can support trauma processing and the cultivation of resilience. Full article

This paper presents a distributed smoothing neurodynamic approach for solving the $L_1$-$L_p$ minimization problem, with application to robust and collaborative multi-view three-dimensional (3D) space localization. To handle the non-Lipschitz continuity gradients, a smooth approximation technique is introduced, yielding a distributed neurodynamic model that integrates classical smoothing neural networks with multi-agents consensus theory. Theoretical analysis guarantees the global convergence of each agent’s state to the optimal solution. The stability and convergence of the proposed approaches are rigorously proved using Lyapunov theory. Numerical experiments on multi-view 3D space localization in the presence of measurement noise demonstrate the method’s effectiveness and practical value for distributed visual computing. Full article

Portfolio optimization is fundamental to modern finance, enabling investors to construct allocations that balance risk and return while satisfying practical constraints. When transaction costs and cardinality limits are incorporated, the problem becomes a computationally demanding mixed-integer quadratic program. This work demonstrates how principles from biomimetics—specifically, the computational strategies employed by biological neural systems—can inspire efficient algorithms for complex optimization problems. We demonstrate that this problem can be reformulated as a constrained quadratic program and solved using dynamics inspired by spiking neural networks. Building on recent theoretical work showing that leaky integrate-and-fire dynamics naturally implement projected gradient descent for convex optimization, we develop a solver that alternates between continuous gradient flow and discrete constraint projections. By mimicking the event-driven, energy-efficient computation observed in biological neurons, our approach offers a biomimetic pathway to solving computationally intensive financial optimization problems. We implement the approach in Python and evaluate it on portfolios of 5 to 50 assets using five years of market data, comparing solution quality against mixed-integer solvers (ECOS_BB), convex relaxations (OSQP), and particle swarm optimization. Experimental results demonstrate that the SNN solver achieves the highest expected return (0.261% daily) among all evaluated methods on the 50-asset portfolio, outperforming exact MIQP (0.225%) and PSO (0.092%), with runtimes ranging from 0.5 s for small portfolios to 8.4 s for high-quality schedules on large portfolios. While current Python runtimes are comparable to existing approaches, the key contribution is establishing a path to neuromorphic hardware deployment: specialized SNN processors could execute these dynamics orders of magnitude faster than conventional architectures, enabling real-time portfolio rebalancing at institutional scale. Full article

The multi-finger robotic hand exhibits significant potential in grasping tasks owing to its high degrees of freedom (DoFs). Object grasping results in a closed-chain kinematic system between the hand and the object. This increases the dimensionality of trajectory tracking and substantially raises the computational complexity of traditional methods. Therefore, this study proposes the discrete finite-time convergent neurodynamics (DFTCN) algorithm to address the aforementioned issue. Specifically, a time-varying quadratic programming (TVQP) problem is formulated for each finger, incorporating joint angle and angular velocity constraints through log-sum-exp (LSE) functions. The TVQP problem is then transformed into a time-varying equation system (TVES) problem using the Karush–Kuhn–Tucker (KKT) conditions. A novel control law is designed, employing a three-step Taylor-type discretization for efficient implementation. Theoretical analysis verifies the algorithm’s stability and finite-time convergence property, with the maximum steady-state residual error being $O\left({\tau }^3\right)$. Numerical simulations illustrate the favorable convergence and high accuracy of the DFTCN algorithm compared with three existing dominant neurodynamic algorithms. The real-robot experiments further confirm its capability for precise grasping, even in the presence of camera noise and external disturbances. Full article

Neurodynamics is recognized as a powerful tool for addressing various problems in engineering, control, and intelligent systems. Over the past decade, neurodynamics-based methods and models have been rapidly developed, particularly in emerging areas such as neural computation and multi-agent systems. In this paper, we provide a brief survey of neurodynamics applied to computation and multi-agent systems. Specifically, we highlight key models and approaches related to time-varying computation, as well as cooperative and competitive behaviors in multi-agent systems. Furthermore, we discuss current challenges, potential opportunities, and promising future directions in this evolving field. Full article

Background: The Upper Limb Neural Tension Test (ULNTT) is a common assessment for neurodynamic function, yet the relationship between ULNTT findings and specific spinal biomechanical patterns remains poorly understood, particularly in the context of cervicobrachial neuralgia. This study aimed to investigate the association between ULNTT asymmetry and cervicothoracic spine biomechanics using advanced motion capture analysis. Methods: A longitudinal experimental study was conducted on two groups of asymptomatic participants: one with ULNTT asymmetry > 10° (AS group, n = 12) and another with symmetrical ULNTT (S group, n = 11). Neurodynamic testing and 3D motion capture of spinal kinematics during head lateral bending were performed at baseline. The AS group then underwent manual medicine intervention targeting spinal mobility impairments, followed by post-intervention reassessment. Spine biomechanics data, focusing on the C5-T4 region, were analyzed using the least squares approximation method to derive parameters describing upper thoracic (T1-T4_VERT) and lower cervical (C5-T1_CONC) lateral bending, and their interrelationship (ANGLE_TANG). Results: At baseline, the AS group showed significant differences between sides in neurodynamic parameters and T1-T4_VERT, with limited upper thoracic lateral bending contralateral to the side of the restricted ULNTT. Significant intergroup differences were also observed for these parameters. Following intervention in the AS group, significant improvements were noted in neurodynamic parameters and T1-T4_VERT, with no significant between-side differences post-intervention. Conclusions: These are preliminary results and preliminary conclusions based on the first study on a small group of patients. Given the limitations, this study provides evidence for a relationship between ULNTT asymmetry and upper thoracic spine biomechanics, specifically a contralateral limitation in lateral bending. These findings suggest a functional link between brachial plexus neurodynamics and upper thoracic spine mobility, offering potential insights into the pathophysiology of cervicobrachial conditions and highlighting the potential role of manual therapy in addressing both neurodynamic and biomechanical impairments. The developed motion capture analysis method offers a novel approach to quantify fine spinal motion patterns. Full article

Quantitative bisimulations between weighted finite automata are defined as solutions of certain systems of matrix-vector inequalities and equations. In the context of fuzzy automata and max-plus automata, testing the existence of bisimulations and their computing are performed through a sequence of matrices that is built member by member, whereby the next member of the sequence is obtained by solving a particular system of linear matrix-vector inequalities and equations in which the previously computed member appears. By modifying the systems that define bisimulations, systems of matrix-vector inequalities and equations with k unknowns are obtained. Solutions of such systems, in the case of existence, witness to the existence of a certain type of partial equivalence, where it is not required that the word functions computed by two WFAs match on all input words, but only on all input words whose lengths do not exceed k. Solutions of these new systems represent finite sequences of matrices which, in the context of fuzzy automata and max-plus automata, are also computed sequentially, member by member. Here we deal with those systems in the context of WFAs over the field of real numbers and propose a different approach, where all members of the sequence are computed simultaneously. More precisely, we apply a simultaneous approach in solving the corresponding systems of matrix-vector equations with two unknowns. Zeroing neural network (ZNN) neuro-dynamical systems for approximating solutions of heterotypic bisimulations are proposed. Numerical simulations are performed for various random initial states and comparison with the Matlab, linear programming solver linprog, and the pseudoinverse solution generated by the standard function pinv is given. Full article

In complex and dynamic environments, traditional pursuit–evasion studies may face challenges in offering effective solutions to sudden environmental changes. In this paper, a bio-inspired neural network (BINN) is proposed that approximates a pursuit–evasion game from a neurodynamic perspective instead of formulating the problem as a differential game. The BINN is topologically organized to represent the environment with only local connections. The dynamics of neural activity, characterized by the neurodynamic shunting model, enable the generation of real-time evasive trajectories with moving or sudden-change obstacles. Several simulation and experimental results indicate that the proposed approach is effective and efficient in complex and dynamic environments. Full article